Multiple access schemes are employed by modern radio systems to allow multiple users to share a limited amount of bandwidth, while maintaining acceptable system performance. Common multiple access schemes include Frequency Division Multiple Access (FDMA), Time Division Multiple Access (TDMA), and Code Division Multiple Access (CDMA). System performance is also aided by error control codes. Nearly all communications systems rely on some form of error control for managing errors that may occur due to noise and other factors during transmission of information through a communication channel. These communications systems can include satellite systems, fiber-optic systems, cellular systems, and radio and television broadcasting systems. Efficient error control schemes implemented at the transmitting end of these communications systems have the capacity to enable the transmission of data including audio, video, text, etc. with very low error rates within a given signal-to-noise ratio (SNR) environment. Powerful error control schemes also enable a communications system to achieve target error performance rates in environments with very low SNR, such as in satellite and other wireless systems where noise is prevalent and high levels of transmission power are costly, if even feasible.
Thus, broad classes of powerful error control schemes that enable reliable transmission of information have emerged including convolutional codes, low density parity check (LDPC) codes, and turbo codes. Both LDPC codes as well as some classes of turbo codes have been successfully demonstrated to approach near the theoretical bound (i.e., Shannon limit). Although long constraint length convolutional codes can also approach the Shannon limit, decoder design complexity prevents practical, wide spread adoption. LDPC codes and turbo codes, on the other hand, can achieve low error rates with lower complexity decoders. Consequently, these codes have garnered significant attention.
Traditionally, LDPC codes have not been widely deployed because of a number of drawbacks. One drawback is that the LDPC encoding technique is highly complex. Encoding an LDPC code using its generator matrix would require storing a very large, non-sparse matrix. Additionally, LDPC codes require large blocks to be effective; consequently, even though parity check matrices of LDPC codes are sparse, storing these matrices is problematic. From an implementation perspective, a number of challenges are confronted. For example, storage is an important reason why LDPC codes have not become widespread in practice. Also, a key challenge in LDPC code implementation has been how to achieve the connection network between several processing engines (nodes) in the decoder. Further, the computational load in the decoding process, specifically the check node operations, poses a problem.
Further, conventional data transmission to and from an ultra small terminal via satellite is usually based on Code Division Multiple Access (CDMA) technique using rate ½ or ⅓ turbo codes. CDMA spreads bandwidth to reduce the interference to adjacent satellites, whereas the turbo code provides coding gain needed to close the link. CDMA also allows multiple users sharing the bandwidth at the same time. However, CDMA systems typically need a large bandwidth expansion factor to function properly. Additionally, CDMA systems require all signals accessing the same spectrum at the same time to be of equal power; provision for power control makes CDMA system more complicated to implement. The inherent long propagation delay of a satellite link makes it even more difficult. Moreover, based on different requirements and regulations that are set (for example, by Federal Communications Commission (FCC), International Radio Union), antenna side lobe, power density at antenna flange, off-axis effective isotropic radiate power (EIRP) density, etc. radiated by terminals that communicate via satellite are limited. However, to provide uplink closure at high data rates using small aperture antenna (for example, in small terminals), the regulatory limits can easily be exceeded by conventional satellite transmission means.
Therefore, there is a need for an access scheme based on LDPC encoding that can effectively utilize low code rates, while minimizing complexity. There is also a need for using LDPC codes efficiently to support high data rates, without introducing greater complexity. There is also a need to improve performance of LDPC encoders and decoders. There is also a need to minimize storage requirements for implementing LDPC coding. There is a further need for a scheme that simplifies the communication between processing nodes in the LDPC decoder. Moreover, there is a need for an access scheme that can effectively spread radiated power spectral density by, for example, utilizing low code rates and spectral spreading, while minimizing complexity